PowerPoint File available:

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BNL_2011.ppt

AcknowledgementsKen Frankel Rick Donahue Howard Padmore Alastair MacDowell

8.3.1 creator: Tom Alber 8.3.1 PRT head: Jamie CateCenter for Structure of Membrane Proteins (PSI)

Membrane Protein Expression Center IICenter for HIV Accessory and Regulatory Complexes

W. M. Keck FoundationPlexxikon, Inc.

M D Anderson CRCUniversity of California Berkeley

University of California San FranciscoNational Science Foundation

University of California Campus-Laboratory Collaboration GrantHenry Wheeler

The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy under contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory.

The optimum wavelength for macromolecular crystallography

Higher? or Lower?

dose

Johns, H. & Cunningham, J. (1974). The physics of radiology. Thomas Springfield, Illinois.

~1 cm at 1 MeV fNH

Charged Particle Equilibrium (CPE)

satisfiesCPE

collimator crystal

X-ray

e-

violatesCPE

Assume a spherical crystal…

is there a “problem” with violating CPE?

ICRU report 31 “Average Energy Required to Produce an Ion Pair” (1979)

for air: W ~ 30 eV/ion-pair

yet, final ions are thermalized (<0.1 eV each)

Where does 99% of the energy go?

Answer: non-ionizing excitations

Secondary ionization

e-

Secondary ionization

e-

e-

+

Excitation

e-

Excitation

e-

Excitation e-

Excitation

ionizing interactions

e- +

Violating CPE: two kinds of “dose”?

non-ionizing interactions

ICRU report 36 “Microdosimetry” (1984)

Charged Particle Equilibrium (CPE)

Johns, H. & Cunningham, J. (1974). The physics of radiology. Thomas Springfield, Illinois.

skin not burned

Ionization track

particle transport simulationusing MCNP

collimator crystal

X-ray

Where do photons go?

beamstop

Transmitted (98%)

Protein1A x-rays


beamstop

elastic scattering (6%)

Transmitted (98%)

Protein1A x-rays

Elastic scattering

Elastic scattering

Inelastic scattering

e-

+


beamstop


Transmitted (98%)

Protein1A x-rays


beamstop


Transmitted (98%)

inelastic scattering (7%)

Protein1A x-rays


beamstop


Transmitted (98%)


Protein1A x-rays

Re-emitted (99%) Absorbed (~0%)

Photoelectric absorption

Photoelectric absorptione-

+


beamstop


Transmitted (98%)


Protein1A x-rays



beamstop


Transmitted (98%)

inelastic scattering (7%) Photoelectric (87%)

Protein1A x-rays



beamstop


Transmitted (98%)

inelastic scattering (7%) Photoelectric (87%)

Protein1A x-rays

Re-emitted (~0%) Absorbed (99%)Re-emitted (99%) Absorbed (~0%)

Fluorescence

+

Fluorescence

e-

+

Auger emission

+

Auger emission

++

e-

MCNP cuts off at 1 keV

1 MeV 100 GJ/mol Medical radiation therapy

100 keV 10 GJ/mol Medical imaging

10 keV 1 GJ/mol X-ray crystallography

1 keV 100 MJ/mol S and P K-edges

100 eV 10 MJ/mol “water window”

10 eV 1 MJ/mol C≡C bond

1 eV 100 kJ/mol C-C bond, visible light

100 meV 10 kJ/mol hydrogen bond

10 meV 1 kJ/mol heat (~300 K)

bonding affects absorption

Almkvist, et al. (2010)."K-edge XANES analysis of sulfur compounds: an investigation of the relative intensities using internal calibration", J. Sync. Rad. 17, 683-688.

MCNP model

particle transport simulationusing MCNP

collimator crystal

X-ray

dose reduction with 1 Å radiation

00.10.20.30.40.50.60.70.80.9

1

0.01 0.1 1 10 100 1000

Crystal diameter (µm)

Dos

e ca

ptur

e fr

actio

n

fNH

←???→

1 keV e- pathlength

100 μm crystal vs energy

00.10.20.30.40.50.60.70.80.9

1

1000 10000 100000 1000000

Photon Energy

Dos

e ca

ptur

e fr

actio

n

1 keV 10 keV 100 keV 1 MeV

fNH

dose reduction vs energy

00.10.20.30.40.50.60.70.80.9

1

1000 10000 100000 1000000

100 um20 um5 um1 um

Photon Energy

Dos

e ca

ptur

e fr

actio

n

1 keV 10 keV 100 keV 1 MeV

2 variablesD

ose

capt

ure

frac

tion

Critical escape diameter

02468

101214161820

0 10000 20000 30000 40000 50000

half

Photon Energy (eV)

Cry

stal

dia

met

er (µ

m)


02468

101214161820

0 10000 20000 30000 40000 50000

half90%

Photon Energy (eV)

Cry

stal

dia

met

er (µ

m)


0.1

1

10

100

1000

10000

1000 10000 100000 1000000 10000000

half90%

Photon Energy

Cry

stal

dia

met

er (µ

m)

1 keV 10 keV 100 keV 1 MeV 10 MeV

Darwin’s Formula

I(hkl) - photons/spot (fully-recorded)

Ibeam - incident (photons/s/m2 )

re - classical electron radius (2.818x10-15 m)

Vxtal - volume of crystal (in m3)

Vcell - volume of unit cell (in m3)

λ - x-ray wavelength (in meters!)

ω - rotation speed (radians/s)

L - Lorentz factor (speed/speed)

P - polarization factor

(1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2

A - absorption factor

exp(-μxtal∙lpath)

F(hkl) - structure amplitude (electrons)

P A | F(hkl) |2I(hkl) = Ibeam re2

Vxtal

Vcell

λ3 LωVcell

Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.

Darwin’s Formula















Vxtal

Vcell

λ3 LωVcell


Darwin’s Formula















Vxtal

Vcell

λ3 LωVcell


Dose Formula

dose - absorbed energy (Gy)

Ibeam - incident (photons/s/μm2 )

texp - exposure time (s)

λ - x-ray wavelength (in Å)

dose ≈ Ibeam ·texp λ2

2000

Dose Formula

Dmax - maximum dose (Gy)


tdataset - accumulated exposure time (s)

λ - x-ray wavelength (in Å)

Dmax ≈ Ibeam ·tdatasetλ2

2000

Dose Formula

Dmax - maximum dose (Gy)


tdataset - accumulated exposure time (s)

R - radius of crystal

Ten - transmission of a sphere ~ exp(-μen·2R)

- density of crystal

Eph - photon energy

qe - electron charge

Dmax = Ibeam ·tdataset

3qeEph

4R(1-Ten)

Darwin’s Formula















Vxtal

Vcell

λ3 LωVcell


Darwin’s Formula

Dmax - maximum dose (kGy)

tdataset - accumulated exposure (s)












P A | F(hkl) |2I(hkl) = re2

Vxtal

Vcell

2 λ LωVcell

Dmax

tdataset


Darwin’s Formula

Dmax - maximum dose (kGy)





2π - rotation range (radians)







P A | F(hkl) |2I(hkl) = re2

Vxtal

Vcell

2 λ L2πVcell

Dmax


Holton & Frankel (2010) Acta D 66 393-408.


Where:IDL - average damage-limited intensity (photons/hkl) at a given resolution105 - converting R from μm to m, re from m to Å, ρ from g/cm3 to kg/m3 and MGy to Gyre - classical electron radius (2.818 x 10-15 m/electron)h - Planck’s constant (6.626 x 10-34 J∙s)c - speed of light (299792458 m/s)fdecayed - fractional progress toward completely faded spots at end of data setρ - density of crystal (~1.2 g/cm3)R - radius of the spherical crystal (μm)λ - X-ray wavelength (Å)fNH - the Nave & Hill (2005) dose capture fraction (1 for large crystals)nASU - number of proteins in the asymmetric unitMr - molecular weight of the protein (Daltons or g/mol)VM - Matthews’s coefficient (~2.4 Å3/Dalton)H - Howells’s criterion (10 MGy/Å)θ - Bragg anglea

2 - number-averaged squared structure factor per protein atom (electron2)Ma - number-averaged atomic weight of a protein atom (~7.1 Daltons)B - average (Wilson) temperature factor (Å2)μ - attenuation coefficient of sphere material (m-1)μen - mass energy-absorption coefficient of sphere material (m -1)

Self-calibrated damage limit

22

sphere2

4425 sin2expsin

4cos301

)2(Tsin2ln

5.0f

f109

2 BM

f

θθ

,R,μT θ ,μ,R λH

VMnλρR

hcrI

a

a

ensphereMrASUNH

decayedeDL


minimum required crystal size

1

1.5

2

2.5

3

3.5

4

4.5

5

1 10 100 1000

photon energy (keV)

crys

tal d

iam

eter

(mic

rons

)

2 A perfect lysozyme

wavelength dependencecr

ysta

l dia

met

er (μ

m)

Å

Minimum size for complete data set

fNH = 1

Where:IDL - average damage-limited intensity (photons/hkl) at a given resolution105 - converting R from μm to m, re from m to Å, ρ from g/cm3 to kg/m3 and MGy to Gyre - classical electron radius (2.818 x 10-15 m/electron)h - Planck’s constant (6.626 x 10-34 J∙s)c - speed of light (299792458 m/s)fdecayed - fractional progress toward completely faded spots at end of data setρ - density of crystal (~1.2 g/cm3)R - radius of the spherical crystal (μm)λ - X-ray wavelength (Å)fNH - the Nave & Hill (2005) dose capture fraction (1 for large crystals)nASU - number of proteins in the asymmetric unitMr - molecular weight of the protein (Daltons or g/mol)VM - Matthews’s coefficient (~2.4 Å3/Dalton)H - Howells’s criterion (10 MGy/Å)θ - Bragg anglea

2 - number-averaged squared structure factor per protein atom (electron2)Ma - number-averaged atomic weight of a protein atom (~7.1 Daltons)B - average (Wilson) temperature factor (Å2)μ - attenuation coefficient of sphere material (m-1)μen - mass energy-absorption coefficient of sphere material (m -1)

Self-calibrated damage limit

22

sphere2

4425 sin2expsin

4cos301

)2(Tsin2ln

5.0f

f109

2 BM

f

θθ

,R,μT θ ,μ,R λH

VMnλρR

hcrI

a

a

ensphereMrASUNH

decayedeDL



0

0.5

1

1.5

2

2.5

3

1 10 100 1000 10000

photon energy (keV)

crys

tal d

iam

eter

(mic

rons

)


Lysozyme with MCNPNave-Hill effect


ysta

l dia

met

er (μ

m)

Å



0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

0 5 10 15 20 25 30 35 40 45 50

photon energy (keV)

crys

tal d

iam

eter

(mic

rons

)


Lysozyme with MCNP Nave-Hill effect


ysta

l dia

met

er (μ

m)

Å



0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

0 5 10 15 20 25 30 35 40 45 50

photon energy (keV)

crys

tal d

iam

eter

(mic

rons

)

3.5 A perfect xtal 100 kDa protein


Lysozyme with MCNP Nave-Hill effect


ysta

l dia

met

er (μ

m)

Å

Å


0.1

1

10

100

100.0 1000.0 10000.0 100000.0 1000000.0 10000000.0

molecular mass

crys

tal d

iam

eter

(um

)

no escape

MCNP

molecular weight

crys

tal d

iam

eter

(μm

)

100 Da 1 kDa 10 kDa 100 kDa 1 MDa 10 MDa


1 ÅX-rays

2 Åspots

B = 24

50% solvent

Prediction:

Exploiting Nave-Hill effect will require multi-crystal datasets

Other reasons for high energy

room temperature

Zero-parallax microscope

pinhole

mirror

microscope

High energy compresses pattern

2 Å data

2 Å data

Example Room-temperature Data

• lysozyme

• 50 μm beam

• 37 Gy/s (0.775 Å)

• 30s exposures at 20C

• 90° of data, 97% complete

• I/ = 1.5 at 1.9 Å

• Rmerge 18% (overall) 5% (low)

• ΔB same as 20 min at 100K

B factor-2

-4

-6

scale vs batch

2

1

0

high energy myth: less background

elastic background/spot intensity ratio is wavelength-independent!

photon energy (eV)

norm

aliz

ed fi

gure

of m

erit

obliquityeffect

high energy myth: less background

elastic background/spot intensity ratio is wavelength-independent!

However: inelastic and fluorescence are less, as is absorption

Other reasons for high energy

room temperature

high pressure?

Room temperature damage rates

0

0.5

1

1.5

2

2.5

0.0001 0.001 0.01 0.1 1 10

Southworth-Davies (lyso)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)

dose rate (kGy/s)

dose

at h

alf i

nten

sity

(MG

y)


0

0.5

1

1.5

2

2.5

0.0001 0.001 0.01 0.1 1 10

powdered lysozymeSouthworth-Davies (lyso)Cheresov (lipid)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)

dose rate (kGy/s)

dose

at h

alf i

nten

sity

(MG

y)

Room temperature damagehas a size dependence?

Radiation Damage “scale factor”

F2 alone

cannot

explain

change

in overall

scale!

Darwin’s Formula














C. G. Darwin (1914)


Vxtal

Vcell

λ3 LωVcell

“scale factor” implies that damaging motions are larger than unit cell

Room temperature damagehas a size dependence?

high pressure will hold it together?

suggests micro-fracture mechanism of spot fading

Radiation Damage prediction

3

exposureps2

kdamage

data

large displacements cannot be faster than the speed of sound

Timescales of radiation damage

Garret et. al. (2005) Chem. Rev. 105, 355-389

Two types of reactions


nonhomogeneous

homogeneous

Timescales of radiation damage


LCLS

ALSbunch


0

0.5

1

1.5

2

2.5

0.0001 0.001 0.01 0.1 1 10

powdered lysozymeSouthworth-Davies (lyso)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)

dose rate (kGy/s)

dose

at h

alf i

nten

sity

(MG

y)


0.01

0.1

1

10

100

1000

0.0001 0.1 100 100000 1E+08 1E+11 1E+14 1E+17 1E+20

powdered lysozymeSouthworth-Davies (lyso)Cheresov (lipid)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)Chapman (2011)

dose rate (kGy/s)

dose

at h

alf i

nten

sity

(MG

y)

Nozzle ground to provide large X-ray diffraction angle

Droplets freeze at 106 o/sec.in vacuumto vitreousice if cryoprotectantadded.

Hand-grinding to micron gives large take-off anglefor X-rays ! D. DePonte

X-rays

5 microns

Flow rate 12 microliters per minute.

An environmental SEM image of operating protein-beam injector for LCLS.

What about very low energy?

sample shadow on detector

Cu

sample shadow on detector

X-ray of cryo stream

low-energy X-rays

Cu

λ=2d sinθ

2.5 Å data with 5 Å X-rays

International Tables for Crystallography, Vol. C, 2nd ed., chapter 6.3

Detecto

r Detector

Detecto

r Detector

d = 2.5 Å d = 2.5 Å

d = 2.5 Åd = 2.5 Å

sam

ple

inje

ctor

Mirr

ors

Mirr

ors

λ = 5 Åd = 2.5 Å

h,k,l

-h,-k,-l

CollidingBeamAnomalousMeasurement

0 20 40 60 80 100

Anomalous differences are resilient to non-isomorphism

Riso (%)

1.0

0.8

0.6

0.4

0.2

0

Cor

rela

tion

Coe

ffici

ent o

f ΔF a

no

100 x 100 lysozyme PDBs

The optimum wavelength for macromolecular crystallography

Maximize data/damage → 15-50 keV

Turn the crank → 12.68 keV

Native element phasing → 2-2.5 keV

the future: multi-crystal data sets

PowerPoint File available:

http://bl831.als.lbl.gov/~jamesh/powerpoint/

BNL_2011.ppt

PowerPoint File available:

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